Is it possible to animate a soft body object?
Yes this is possible

First create a floor cube large wide but not that high.
Make it a Passive rigid body.  (so it wont fall down its the floor)

Next a bit above it add a cube, subdivide it a few times.
First add rigid body collision (convex hull, source deform).
Next add softbody to this cube.

It will drop and woble on the floor.

oh and for better results use damping on soft body.
such cubes can bounche on eachother as well if you copy them shift D